LMFDB - Newform orbit 882.4.a.s

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(1,882)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("882.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q + 2 q^{2} + 4 q^{4} + 22 q^{5} + 8 q^{8}+O(q^{10}) $

$ q + 2 q^{2} + 4 q^{4} + 22 q^{5} + 8 q^{8} + 44 q^{10} - 26 q^{11} + 54 q^{13} + 16 q^{16} + 74 q^{17} - 116 q^{19} + 88 q^{20} - 52 q^{22} + 58 q^{23} + 359 q^{25} + 108 q^{26} - 208 q^{29} + 252 q^{31} + 32 q^{32} + 148 q^{34} + 50 q^{37} - 232 q^{38} + 176 q^{40} + 126 q^{41} + 164 q^{43} - 104 q^{44} + 116 q^{46} - 444 q^{47} + 718 q^{50} + 216 q^{52} - 12 q^{53} - 572 q^{55} - 416 q^{58} + 124 q^{59} + 162 q^{61} + 504 q^{62} + 64 q^{64} + 1188 q^{65} - 860 q^{67} + 296 q^{68} + 238 q^{71} + 146 q^{73} + 100 q^{74} - 464 q^{76} - 984 q^{79} + 352 q^{80} + 252 q^{82} + 656 q^{83} + 1628 q^{85} + 328 q^{86} - 208 q^{88} - 954 q^{89} + 232 q^{92} - 888 q^{94} - 2552 q^{95} - 526 q^{97}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

1.1

2.00000

4.00000

22.0000

8.00000

44.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$-1$
$3$	$1$
$7$	$-1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	882.4.a.s		1
3.b	odd	2	1		882.4.a.a		1
7.b	odd	2	1		126.4.a.f	yes	1
7.c	even	3	2		882.4.g.a		2
7.d	odd	6	2		882.4.g.m		2
21.c	even	2	1		126.4.a.e	✓	1
21.g	even	6	2		882.4.g.n		2
21.h	odd	6	2		882.4.g.x		2
28.d	even	2	1		1008.4.a.a		1
84.h	odd	2	1		1008.4.a.w		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
126.4.a.e	✓	1	21.c	even	2	1
126.4.a.f	yes	1	7.b	odd	2	1
882.4.a.a		1	3.b	odd	2	1
882.4.a.s		1	1.a	even	1	1	trivial
882.4.g.a		2	7.c	even	3	2
882.4.g.m		2	7.d	odd	6	2
882.4.g.n		2	21.g	even	6	2
882.4.g.x		2	21.h	odd	6	2
1008.4.a.a		1	28.d	even	2	1
1008.4.a.w		1	84.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(882))$:

$ T_{5} - 22 $

$ T_{11} + 26 $

$ T_{13} - 54 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T $ T
$5$	$ T - 22 $ T - 22
$7$	$ T $ T
$11$	$ T + 26 $ T + 26
$13$	$ T - 54 $ T - 54
$17$	$ T - 74 $ T - 74
$19$	$ T + 116 $ T + 116
$23$	$ T - 58 $ T - 58
$29$	$ T + 208 $ T + 208
$31$	$ T - 252 $ T - 252
$37$	$ T - 50 $ T - 50
$41$	$ T - 126 $ T - 126
$43$	$ T - 164 $ T - 164
$47$	$ T + 444 $ T + 444
$53$	$ T + 12 $ T + 12
$59$	$ T - 124 $ T - 124
$61$	$ T - 162 $ T - 162
$67$	$ T + 860 $ T + 860
$71$	$ T - 238 $ T - 238
$73$	$ T - 146 $ T - 146
$79$	$ T + 984 $ T + 984
$83$	$ T - 656 $ T - 656
$89$	$ T + 954 $ T + 954
$97$	$ T + 526 $ T + 526
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Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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